Basics of Number System -Decimal Number, Binary Number, Octal Number and Hexa Decimal Number .
The number system is a way of
representing and expressing numerical quantities. They provide a systematic
method for calculating, computing and performing mathematical activities.
Various number systems have been developed throughout history, but the most commonly
used systems today are decimal systems (base-10), binary systems (base-2),
octal systems (base-8), and hexadesimal systems (base-16).
Here is a brief explanation of each
number system:
1. 1. Decimal
system (Base-10):
The decimal system is the most
familiar number system and is used in our daily lives. It has ten digits from 0
to 9. The value of each digit is determined by its position in the number. The
exact digit represents the space, the next digit represents ten places, then
hundreds of places, etc. For example, the number 342 in the decimal system
represents 3 percentiles, 4 tens and 2.
2. Binary system (Base-2): Only two
digits, 0 and 1 are used in binary systems. It is widely used in computers and
digital systems because of its simplicity in representing data electronically.
In binaries, the value of each digit is determined by its state, as in the
decimal system. However, each condition represents an increased power of 2
instead of 10. For example, binary number 1011 represents 1 * 2^3 + 0 * 2^2 + 1
* 2^1 + 1 * 2^0, which is equal to 11 in decimals.
3. Octal System (Base-8): The octal
system uses eight digits from 0 to 7. It is less commonly used today but still
has applications in some areas, such as computer programming and electronics.
As in the decimal system, the value of each digit in the octal is determined by
its position. Each condition represents an increased power of 8. For example,
octal number 63 at 6 * 8^1 + 3 * 8^0 represents, which is equal to 51 on
decimals.
4. Hexadesimal System (Base-16):
Sixteen digits are used in the hexadesimal system: 0 to 9 and from A to F,
where A represents 10, represents B11, and thus up to F, which represents 15.
Hexadecimal is widely used in computer programming, especially in representing
memory addresses and colors. As with other number systems, the value of each
digit in hexadesimal is determined by its position. Each condition represents
an increased power of 16. For example, the hexadecimal number 2F represents 2 *
16^1 + F * 16^0, which is equal to 47 at the decimal.
These number systems serve different purposes and have unique advantages in different fields. Understanding different number systems when working with and calculating different types of data can be helpful for computer scientists, programmers, engineers, and mathematicians.
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